score:3
Most toll authorities that allow billing by mail have websites where you can look up your account by license plate number. It can sometimes take several weeks for what you owe to appear on the site.
I'd suggest googling "toll" and the name of your bridge to find out the toll authority responsible, and there you should be able to find the details of how they do billings, and figure out the status of your account.
In some situations I've found that bills are never sent to vehicle owners from certain jurisdictions (e.g. I found out by experience that the Highway 407 toll authority in Toronto and the Washington state toll authority in the Seattle area don't bill vehicles from Saskatchewan, presumably because they see so few of them that they choose not to pay the fees to get license information from such vehicles.)